摘要
此篇論文是以發展微小化揚聲器應用於可攜式裝置為其目標，因此輕薄、效率高和體積小的特性乃是非常重要的。其中聚偏氟乙烯因為其輕薄且轉換效率高的特性，很適合應用在可攜式產品上，為了將壓電薄膜於平面上的應變轉換成橫向的位移，因此給予壓電薄膜微量的彎曲，而為了有助於我們對於喇叭的最佳化設計，一個複合的類比電路模擬平台將會被建立，主要是以集中參數法的架構為基礎，以解析解的輻射阻抗配合有限單位法的分析方法去模擬電路中機械端的阻抗，如此便能有效預測喇叭的高頻模態。從模擬結果顯示，隨著曲率半徑的下降，音壓大小和共振頻率會隨之增大。為了辨識集中參數，一連串辨識的流程被發展出來，藉由電端的阻抗量測，電端的等效電容值可以被估測出來，而機械端的阻抗和耦合係數可以利用雷射量測薄膜的振動速度而求得，如此集中參數便能被辨識出來，進而完成類比電路的模型。接著為了最佳化喇叭的參數，在這裡被使用了模擬退火法。從結果可以看出經由最佳化的設計聲壓提升了15分貝，且低頻也因此延伸到了700赫茲。
然而聚偏氟乙烯若要應用到小型的可攜式產品，像是手機或隨身聽，因為其要求的面積較大，則不太適合。在這裡要再介紹平衡電樞式揚聲器，因為其體積較小，且其機電耦合係數較大，非常具有潛力於應用在可攜式產品。經過機電耦合關係的推導之後，我們發現機電耦合因子是對稱的，這代表過去應用在動圈式揚聲器的類比電路也可以應用在平衡電樞式揚聲器，而參數辨識的方法也是一樣的，這表示我們以建立好一個電樞式揚聲器的類比電路模型，而過去的最佳化方法也可以應用在對其的最佳化設計上。

This study is to develop miniaturizing loudspeakers for handheld devices, where the thinness, volume and efficiency of the loudspeaker are the major concerns. Polyvinylidene fluoride (PVDF) loudspeaker is one of the candidates for its properties of thin and efficiency. The membrane of PVDF loudspeaker is slightly curved in order to convert in-plane strains into transverse ones. To facilitate the design optimization, a simulation platform is established with a hybrid analogous circuit. While the circuit is primarily a lumped parameter in nature, the mechanical impedance can be derived from a finite-element analysis. The mechanical impedance, along with a more precise model of radiation impedance, enables the prediction of the high order modes of the loudspeaker. The simulation results indicate that a reduced radius of curvature leads to an increased sound pressure level and a higher resonance frequency. To identify the lumped parameters, a series of special procedures is developed. Based on the measurement of electrical impedance, the electrical capacitance is estimated. The mechanical parameters and the coupling factor are identified through the measurement of diaphragm velocity with a laser vibrometer. To optimize the design parameters of the loudspeaker, the simulated annealing (SA) algorithm is used under practical constraints. The results have shown that, with the optimal configuration, the sound pressure level increases by 15 dB and the resonance
III
frequency increases by 700 Hz, as compared with a non-optimal design. Although the PVDF loudspeaker is thin and efficient, the area it required is too large for handheld devices. BA speaker take the advantages of tiny size and stronger electro-mechanical coupling coefficient, let it be a choice of high potential. After deriving the electro-mechanical coupling coefficient of BA speaker, the EMA model of BA speaker is found that it is identical to the one of moving-coil speaker. The ID procedure and optimal method used before can apply to it as moving-coil loudspeaker. A platform of optimal design for BA speaker is established.

TABLE OF CONTENTS
摘要................................................................................................................................ I
ABSTRACT ................................................................................................................. II
誌謝.............................................................................................................................. IV
List of Tables .............................................................................................................. VI
List of Figures ........................................................................................................... VII
CHAPTER 1 Introduction .................................................................................... 1
CHAPTER 2 Modeling ........................................................................................ 4
2.1 Electrical-mechanical-acoustical Analogous Circuits ........................... 5
2.2 Modeling of Acoustical System ............................................................. 5
2.2.1. Acoustic Compliance ..................................................................... 6
2.2.2. Radiation Impedance of a Baffled Rigid Piston ............................ 7
CHAPTER 3 PVDF Loudspeaker ................................................................... 12
3.1. Modeling of PVDF Loudspeaker ......................................................... 13
3.2. Parameters Identification ..................................................................... 14
3.3. Finite Element Analysis of the PVDF Membrane Assembly .............. 17
3.4. Design of Optimization ........................................................................ 18
3.4.1. Simulated Annealing (SA) Algorithm ......................................... 18
3.4.2. Optimization of PVDF Loudspeaker ........................................... 19
3.5. Simulation and Experiment.................................................................. 20
CHAPTER 4 Balanced armature speaker ...................................................... 39
4.1. Modeling of BAS and Loudspeaker with New Structure .................... 40
4.2. Parameters Identification of BAS ........................................................ 42
4.3. Simulation and Experiment.................................................................. 43
CHAPTER 5 Conclusions ................................................................................. 51
References ................................................................................................................... 53

1 C. I. Tseng and W. J. Liou, “Simulation of a bimorph transducer under acoustic excitation,” Computers & Structures, 59, 141-148 (1996).
2 A. B. Dobrucki and P. Pruchnicki, “Theory of piezoelectric axisymmetric bimorph,” Sensors and Actuators A, 58, 203-212 (1997).
3 Q Wang, S. T. Quek, C. T. Sun, and X Liu, “Analysis of piezoelectric coupled circular plate,” Smart Mater. Struct., 10, 229-239 (2001).
4 B. Aronov, “The energy method for analyzing the piezoelectric electroacoustic transducers,” J. Acoust. Soc. Am., 117, 210-220 (2005).
5 B. Aronov, “The energy method for analyzing the piezoelectric electroacoustic transducers II. (With the examples of the flexural plate transducer),” J. Acoust. Soc. Am., 118, 627-637 (2005).
6 M. R. Bai and Y. Lu, “Optimal implementation of miniature piezoelectric panel speakers using the Taguchi method and Genetic algorithm,” Journal of Vibration and Acoustics, 126, 359-369 (2004).
7 F. L. Wen, S. C. Mou, and M. Ouyang, “Design and construction of shaft-driving type piezoceramic ultrasonic motor,” Ultrasonics, 43, 35-47 (2004).
8 A. Caronti, G. Caliano, and M. Pappalardo, “An accurate model for capacitive micromachined ultrasonic transducers,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 49, 159-168 (2002).
9 Q. Gallas, R. Holman, T. Nishida, B. Carroll, M. Sheplak, and L. Cattafesta, “Lumped element modeling of piezoelectric-driven synthetic jet actuators,” AIAA Journal, 41, 240-247 (2003).
54
10 A. Duclos, B. Gazengel, N. Lhermet, and G. Milot, “Study of a dome shaped PVDF loudspeaker,” Cedrat Technologies (2004).
11 Piezoelectric Polymer Speaker (1998) Measurement Specialties Inc., Application Note 1242138 Rev. B; Piezo Film Sensors Technical Manual (1999), ibid, P/N 1005665663-1 Rev
12 M. R. Bai and C. J. Wang, “Experimental modeling and design optimization of push-pull electret loudspeakers,” J. Acoust. Soc. Am., 127(4), 2274-2281 (2010).
13 Aarts, R. M. and Janssen, A. J. E. M. "Approximation of the Struve Function Occurring in Impedance Calculations." J. Acoust. Soc. Amer. 113, 2635-2637, 2003.
14 M. R. Bai, C. Y. Liu, and R. L. Chen, “Optimization of microspeaker diaphragm pattern using combined finite element–lumped parameter models,” IEEE Transactions On Magnetics, 44, 2049-2057 (2008).